Job sequencing on 3 machines.

1
Job sequencing on 3 machines.

• Two conditions for a easy solution
• 1. The smallest duration on machine 1 is at
  least as great as the largest duration on machine
  2.
• 2. The smallest duration on machine 3 is at
  least as great as the largest duration on machine
  2.

2
Conditions for an easy solution

• T1,smallest gt T2,largest
• AND/OR
• T3,smallest gt T2,largest

3
The easy solution how-to...

• Add T1 T2 T2 T3
• Use these sums to do Johnsons rule.

4
Example 3 machines

• Duration (hrs.)
• Job Mach 1 Mach 2 Mach 3
• B 5 3 7
• A 13 5 9
• C 6 4 5
• D 7 2 6

5
Example 3 machines
One of the conditions is met.

• Duration (hrs.)
• Job Mach 1 Mach 2 Mach 3
• A 13 5 9
• B 5 3 7
• C 6 4 5
• D 7 2 6

6
Example 3 machines

• Duration (hrs.)
• Job Mach 12 Mach 23
• A 135 59
• B 53 37
• C 64 45
• D 72 26

7
Example 3 machines

• Duration (hrs.)
• Job Mach 12 Mach 23
• A 18 14
• B 8 10
• C 10 9
• D 9 8

8
Example 3 machines

• Duration (hrs.)
• Job Mach 12 Mach 23
• A 18 14
• B 8 10
• C 10 9
• D 9 8

B goes first.
9
Example 3 machines

• Duration (hrs.)
• Job Mach 12 Mach 23
• B 8 10
• A 18 14
• C 10 9
• D 9 8

D goes last.
10
Example 3 machines

• Duration (hrs.)
• Job Mach 12 Mach 23
• B 8 10
• A 18 14
• C 10 9
• D 9 8

C goes next-to-last.
11
Example 3 machines

• Duration (hrs.)
• Job Mach 12 Mach 23
• B 8 10
• A 18 14
• C 10 9
• D 9 8

B goes 3rd-to-last.
12
Ex 3 machines Gantt Chart

• Duration (hrs.)
• Job Mach 1 Mach 2 Mach 3
• B 5 3 7
• A 13 5 9
• C 6 4 5
• D 7 2 6

Time (hrs.) gt
B
B
B
13
Ex 3 machines Gantt Chart

• Duration (hrs.)
• Job Mach 1 Mach 2 Mach 3
• B 5 3 7
• A 13 5 9
• C 6 4 5
• D 7 2 6

Time (hrs.) gt
B
A
B
A
B
A
14
Ex 3 machines Gantt Chart

• Duration (hrs.)
• Job Mach 1 Mach 2 Mach 3
• B 5 3 7
• A 13 5 9
• C 6 4 5
• D 7 2 6

Time (hrs.) gt
B
A
C
B
A
C
B
A
C
15
Ex 3 machines Gantt Chart

• Duration (hrs.)
• Job Mach 1 Mach 2 Mach 3
• B 5 3 7
• A 13 5 9
• C 6 4 5
• D 7 2 6

Time (hrs.) gt
B
A
C
D
B
A
C
D
B
A
C
D
16
Ex 3 machines Gantt Chart

• Duration (hrs.)
• Job Mach 1 Mach 2 Mach 3
• B 5 3 7
• A 13 5 9
• C 6 4 5
• D 7 2 6

43
31
33
37
24
28
5
8
15
18
23
32
B
A
C
D
B
A
C
D
B
A
C
D